AC 20-191

AC 20-191 Appendix B L σ2 ( 2w1+ 2.67 1.339L Ω) Ω w w ) wΦ ( =  ( ) 112 62π1+ 1.339L Ω  w  where:

= spectral density in (ft./sec)2 Φ w σw = root mean square (rms) turbulence magnitude in ft/sec = 0.1061V20(ft/sec).

Where V 20 i s expressed in ft/sec.

Lw = scale length = h (for h < 1000 ft) Ω = spatial frequency in radians/ft = ω/VT ω = temporal frequency in radians/sec, and VT = aircraft speed in ft./sec.

B.2.3.2. Horizontal Component of Turbulence:

The horizontal component of turbulence consists of a longitudinal component (in the direction of the mean wind) and lateral component (see Figure B-5). The longitudinal and lateral components have spectra of the form defined by the following equations:

B.2.3.2.1 Longitudinal Component:

( ) L σ2Φu Ω = ( u u π 1+(1.399ΩLu) 2 ) 56 B.2.3.2.2 Lateral Component:

L 2v σv (1+ 2.67(1.339L Ω)2 ) Φv(Ω) v = 2 ( +( 11 π 1 1 .339L 2 ) 6 vΩ) B-2

AC 20-191 Appendix B B.2.3.3. Turbulence Intensities and Scale Lengths.

The RMS turbulence intensities are defined as below σw = 0.1061V 20 (ft/sec)

• When h≥1,000ft. σ = σ = σ u v w

• When h<1,000ft.

0.4  σ =σ =σ  u v w  0.177+ 0.000823h 

• When h≤0ft.

 1 

0.4 σ =σ =σ u v w  0.177 The turbulence scales are defined as below

• When h≥1,000ft. L = L = L = 1,000 u v w

• When h<1,000ft L = h w  1 

1.2 L = L = h u v ( 0.177+ 0.000823h)

• When h≤0ft. L = L = L = 0 u v w B-3

AC 20-191 Appendix B Figure B-1 Headwind-Tailwind Probability of Exceedance, %

99.99 99.9 99 90 80 70 60 50 40 30 20 0.01 30 TAILWIND SPEED .KT (WIND FROM 180 DEG) 10 HEADWIND SPEED .KT (WIND FROM O DEG) -300.01 0.1 10 20 30 40 50 60 70 80 90 99 99.9 99.99 Probability of not Exceeding, %

HEADWIND-TAILWIND DESCRIPTION B-4

AC 20-191 Appendix B Figure B-2 Crosswind CROSSWIND SPEED.KT COUNTERCLOCKWISE FROM 0 DEG 99.99 99.9 99 90 Probability of Exceedance, % 80 70 60 50 40 30 10 0.1 0.01 30

0.1 20 30 40 50 60 70 80 99 99.9 99.99 _ Probability of Exceedance, %

CROSSWIND DESCRIPTION B-5

AC 20-191 Appendix B Figure B-3 Annual Percent Probability of Mean Wind Speed Equaling or Exceeding Given Values PERCENT PROBABILITY OF EXCEEDANCE 20

0.2

o. O 5 10 15 20 25 30 35 40 Wind Speed Tw kt

ANNUAL PERCENT PROBABILITY OF MEAN WIND SPEED

EQUALING OR EXCEEDING GIVEN VALUES 9-&

AC 20-191 Appendix B Figure B-4 Wind Direction Relative to Runway Heading Wind Direc tion Histog ra m Wind Direction Rela tive to Runwa y Hea ding P e r c e n t 0 2 4 6 8 10 12 180190200210220230240250260270280290300310320330340350 0 10 20 30 40 50 60 70 80 90 100110120130140150160170180

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Wind fr om the L eft Wind from the R ight B-7

AC 20-191 Appendix B Figure B-5 Selected Description for Variances of Horizontal Turbulence Components.

— f[0.177+0.823hh ¡] ‡ h≤h¡

1.0 mani

1.2

1.0

0.8 h/h j 0.6

0.2

1.0 1.2 1.6 2.0 B-8

AC 20-191 Appendix B Figure B-6 Selected Integral Scale Description.

Lw =1 d,h = hi h,h<hi LWoU h h < hj Lu ={ Ow I 10.177 + 0.823 h/t ] 1.2 d nzhi Ly=Lu hj= Altitude above which turbulence is isotropic

1.2 Г

1.0

0.8 h/h¡

0.6

0.4 L=L

0.2

0.2 0.4 0.6 0.8 1.0 Lw/h¡›Lu/h¡= Lv/h¡

SELECTED INTEGRAL SCALE DESCRIPTION В-9

AC 20-191 Appendix B B.3 Wind Model C.

This wind model is a harmonized derivative of Wind Model A incorporating the changes defined in JAA paper AWOG 904a. The changes are a result of experience from pilot-in-the-loop simulator tests for Category III HUD certification, where the wind shear and turbulence intensities defined in JAA paper AWOG 904a were found to be more representative of nominal wind conditions for Category III approaches and compatible with motion-based, pilot-in-the-loop simulators. Wind Model C is therefore more appropriate for use in Category III HUD certification programs; however, this does not preclude its use for other types of landing system.Wind Shear (Vwref).

B.3.2 The Model A equation for the Wind Shear component:

 h+ 0.15V = 0.20407 V ln wref 20  0.15  is replaced for Wind Model C with:

 h+ 0.046Vwref = 0.165 V20 ln  0.046  B.3.3 Root-Mean-Square (RMS) Turbulence Scale (σw).

The Model A equation for the RMS Turbulence Scale: σw = 0.1061V20 (ft/sec) is replaced for Wind Model C with: σw = 0.0625V20 (ft/sec) B.3.4 Turbulence Scale Factor (Lu).

The Model A establishes three values for Turbulence Scale Factor Lu depending on the altitude h, but for Model C, Lu = 600 feet, for all values of h B.4 Wind Model B.

B.4.1 Mean Wind.

It may be assumed that the cumulative probability of reported mean wind speed at landing and the crosswind component of that wind are as shown in Figure B-7.

Normally, the mean wind that is reported to the pilot is measured at a height that may be between 20 ft.(6m) and 33 ft. (10m) above the runway. The models of wind shear and turbulence given in the following paragraphs assume this reference height.

B.4.2 Wind Shear.

Wind shear should be included in each simulated approach and landing unless its effect can be accounted for separately. The magnitude of the shear should be defined by the expression:

u = 0.43 U log10 (z) + 0.57 U, for z ≥ 0.05 m u≅ 0, for z < 0.05m where z is the height in meters u is the mean wind speed at height z (meters) B-10

AC 20-191 Appendix B U is the mean wind speed at 10m (33 ft.).

B.4.3 Abnormal Wind Shear.

The effect of wind shears exceeding those described above should be investigated using known severe wind shear data.

B.4.4 Turbulence.

B.4.4.1. Horizontal Component of Turbulence.

It may be assumed that the longitudinal component (in the direction of mean wind) and lateral component of turbulence may each be represented by a Gaussian process having a spectrum of the form:

( ) 2σ2 LΦ Ω = •π 1+Ω 2 L2 where Φ(Ω) = a spectral density in (meters/sec)2 per (radian/meter).

σ = root mean square (rms) turbulence intensity = 0.15 U L = scale length = 183m (600 ft.)

Ω = spatial frequency in radians/meter.

B.4.4.2. Vertical Component of Turbulence.

It may be assumed that the vertical component of turbulence has a spectrum of the form defined by the equation above for the horizontal component with the following values:

σ = 1.5 knots with L = 9.2m (30 ft.), or alternatively σ = 0.09 U with L = 4.6m (15 ft.) when z < 9.2m (30 ft.), and L = 0.5 z when 9.2 < z < 305m (30 < z < 1000 ft.)

B-11

AC 20-191 Appendix B Figure B-7 Cumulative probability of reported Mean Wind, and Head Wind, Tail Wind Cross Wind Components when landing.

403020100 Total Wind Head Wind ComponentCross Wind Component Tail Wind Component

WIND SPEED KNOTS Cumulative probability of reported Mean Wind, and Head Wind, Tail Wind Cross Wind Components, when landing.

P R O B A B I L I T Y O F E X C E E D I N G G I V E N W I N D S P E E D

0.01

0.05

0.1

0.2

0.5 1 2 8 10 20 30 40 50 60 70 80 90 95 98 99

99.8

99.9

99.99 NOTE: This data is based on world wide in-service operations of UK airlines (sample size about 2000) B-12

AC 20-191 Appendix B B.5 Acronyms and Definitions for the Wind Models.

h Height AGL in ft.

Lu Turbulence scale factor RMS Root Mean Square VT Aircraft speed in ft/sec.

Vwref Mean wind speed measured at h ft V20 Mean Wind speed measured at 20 ft. AGL w Temporal frequency in radians/sec, σw RMS turbulence scale in knots W Spatial frequency in radians/ft.

Φw(Ω) Spectral density of the vertical component of turbulence in (ft/sec)2 B-13